The specs on either aren't great and most likely will struggle to run 'high' at 30FPS, especially on Fallout 4 and Battlefield 4. It just about meets the minimum requirements for Fallout 4, Battlefield 4, and Battlefront (2015), and barely even touches the recommended which is suggested to reach 'medium/high' graphics options.
4GB RAM isn't great for gaming really but it should get by as long as you don't host any matches.
CPU will struggle but will probably make do, but with GPU specs like that I don't think the CPU will be the main issue here.